A magnetometer that finds a magnitude of an ambient magnetic field, comprising: a) a diamond cubic structure crystal, with an ensemble of paramagnetic defects oriented along each of the crystal's four tetrahedral axes; b) a microwave source that produces a microwave field at the crystal, of controllable frequency over a range that includes microwave resonance frequencies of paramagnetic defects oriented along all four axes; c) a light source that illuminates the paramagnetic defects with light that causes fluorescent emission from the paramagnetic defects; d) a light detector that measures the fluorescent emission; and e) a controller configured to: 1) measure the fluorescent emission at different microwave frequencies within the range, to obtain a spectrum of the paramagnetic defect ensemble; 2) calculate a variance property of the spectrum; and 3) calculate the magnitude of the ambient magnetic field from the variance property.

A magnetometer that finds a magnitude of an ambient magnetic field, comprising: a) a diamond cubic structure crystal, with an ensemble of paramagnetic defects oriented along each of the crystal's four tetrahedral axes; b) a microwave source that produces a microwave field at the crystal, of controllable frequency over a range that includes microwave resonance frequencies of paramagnetic defects oriented along all four axes; c) a light source that illuminates the paramagnetic defects with light that causes fluorescent emission from the paramagnetic defects; d) a light detector that measures the fluorescent emission; and e) a controller configured to: 1) measure the fluorescent emission at different microwave frequencies within the range, to obtain a spectrum of the paramagnetic defect ensemble; 2) calculate a variance property of the spectrum; and 3) calculate the magnitude of the ambient magnetic field from the variance property.